This invention relates to phase locked loops and, more particularly, to phase locked loops for use with single phase circuits.
The control circuits of many types of power electronic equipment need a stable, accurate reference of the angle of the input power for use by other parts of the control. A phase-locked loop (PLL) is often used for this purpose. In a single phase system, it is difficult to derive a phase reference which does not have cycle-by-cycle phase modulation (jitter) unless noise sensitive edge triggered methods or very heavy, and therefore slowly responding, loop filters are used.
In three phase systems, it is possible to vectorially sum components of the three phase voltages to obtain a quadrature set of sine waves which can be used by the phase comparator of a PLL to generate a phase error signal which has a constant value proportional to the sine of the input phase angle minus the voltage controlled oscillator (VCO) phase angle and (optionally) plus a constant. For example, if a direct component derived from the three phase input is proportional to sin(a) and the quadrature component is proportional to -cos(a), the phase error can be calculated as follows: ##EQU1## where "a" is the phase angle of the line and "b" is the phase angle of the VCO. Other implementations with different steady state phase shifts are also possible.
In the ideal case, the phase error has no ripple after settling and no phase modulation of the VCO will result. Even in a practical system, the ripple which results from negative sequence and harmonic voltages is small and only slight filtering is usually required. In a single phase system, it is not possible to use vector summation to construct a quadrature set of sine waves. No scaling can make a sine wave out of a cosine wave since they are orthogonal. A phase comparator can be constructed without quadrature inputs, but the output will have a large ripple component at twice the input frequency in the steady state. Although the DC average of the phase comparator output is proportional to the sine of the phase error, the ripple can cause objectionable phase modulation even when heavy filtering is used. For example, if the input to the PLL is proportional to cos(a) and the VCO output is cos(b), then: ##EQU2##
In the steady state, the frequency of a and b will be the same, only a phase angle difference (possibly zero) will exist. In that event: ##EQU3##
In the above equations, the phase error consists of a DC term proportional to the cosine of the angular difference and a twice frequency ripple term of significant magnitude.
Some means of phase shifting using delays, filters or integrators can be used to develop a quadrature set of inputs. However, these techniques do not provide satisfactory performance. This invention seeks to provide an accurate and stable source of the angle of an input sine wave for use in controlling single phase power electronic equipment or other control systems requiring filtered angle references.